Flaws

Do you consider the first-move-advantage and the high amount of draws at top-level to be flaws?

No. I'm not sure if there is an advantage in moving first? And I think the draws at top-level chess is their problem, if it is a problem? Some of my favourite games I have played have ended in draws. I like the ability to draw:)

I would consider a draw with you Sharon a great game... if that could ever happen. :)

I once read somewhere that at GM level of chess, playing black is a disadvantage though very small. White wins 50.something % of the time vs. black's 49.something % of the time. 

I know that from a psychological perspective a draw is a fine result.

But in order to measure who is better it's quite impractical.

Also the winning-percentage discrepancy is a lot bigger than what you are saying.

From Wikipedia:

Could you imagine a tournament that in the first rounds has single-elimination and for finals something like best of 3 and best of 5?

I couldn't.

Can't blame someone who has lived thousands of years ago for bad game-design, but I feel like it could be done better and consider it at least somewhat flawed by todays standards.

At lower levels of play, the advantage of playing white is very small. At GM level, however, there is a huge difference. Just look in the Game Explorer, white usually has around a 10% higher win probability than black.